Explore Transformations:
Activity 1
I. Exploration I
1.
Enter: 𝑦2 = 𝑦1 + 1
Enter the following functions, one at a time, into 𝑦1.
Sketch the graph 𝑦1 of and 𝑦2 on the same coordinate plane.
a.)
𝑦1 = |𝑥|
c.)
𝑦1 =
e.)
𝑦1 =
𝑥
3
𝑥
2
b.)
𝑦1 = 𝑥
d.)
𝑦1 = 𝑥
3
Explore Transformations:
2.
Activity 1
Enter: 𝑦2 = 𝑦1 − 2
a.)
𝑦1 = |𝑥|
c.)
𝑦1 =
e.)
𝑦1 =
𝑥
3
𝑥
2
b.)
𝑦1 = 𝑥
d.)
𝑦1 = 𝑥
3
Explore Transformations:
3.
Activity 1
Describe in detail what happens to the following characteristics of the graphs
when you add or subtract a constant from the function rule, comparing and
contrasting 𝑦1 and 𝑦2.
a.)
Domain
B.)
Range
c.)
Intervals of Increasing/Decreasing
d.)
End Behavior
e.)
Odd or Even symmetry
Explore Transformations:
Activity 1
II. Exploration II
4.
Enter: 𝑦2 = 𝑦1(𝑥 − 1)
Enter the following functions, one at a time, into 𝑦1.
Sketch the graph 𝑦1 of and 𝑦2 on the same coordinate plane.
a.)
𝑦1 = |𝑥|
c.)
𝑦1 =
e.)
𝑦1 =
𝑥
3
𝑥
2
b.)
𝑦1 = 𝑥
d.)
𝑦1 = 𝑥
3
Explore Transformations:
5.
Activity 1
Enter: 𝑦2 = 𝑦1(𝑥 + 2)
a.)
𝑦1 = |𝑥|
c.)
𝑦1 =
e.)
𝑦1 =
𝑥
3
𝑥
2
b.)
𝑦1 = 𝑥
d.)
𝑦1 = 𝑥
3
Explore Transformations:
6.
Activity 1
Describe in detail what happens to the following characteristics of the graphs
when you replace x with x - a, comparing and contrasting 𝑦1 and 𝑦2.
a.)
Domain
B.)
Range
c.)
Intervals of Increasing/Decreasing
d.)
End Behavior
e.)
Odd or Even symmetry